The equation of a circle $C$ is $x^2+y^2+2x+6y-15 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2+2x) + (y^2+6y) = 15$ $(x^2+2x+1) + (y^2+6y+9) = 15 + 1 + 9$ $(x+1)^{2} + (y+3)^{2} = 25 = 5^2$ Thus, $(h, k) = (-1, -3)$ and $r = 5$.